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• W2034429858 abstract "Infrared divergences in scattering amplitudes arise when a loop momentum ℓ becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in $ mathcal{N} = {4} $ super-Yang-Mills theory enjoy softer than expected behavior as ℓ ∥ p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively. PDF and Mathematica files with all of our results are provided at http://goo.gl/qIKe8 ." @default.
• W2034429858 created "2016-06-24" @default.
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• W2034429858 date "2012-03-01" @default.
• W2034429858 modified "2023-09-24" @default.
• W2034429858 title "The soft-collinear bootstrap: $ mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops" @default.
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• W2034429858 doi "https://doi.org/10.1007/jhep03(2012)032" @default.
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